Since someone asked me why I haven't written one of my "too long" answers to this, its because I don't have the time. I might on Monday if someone else doesn't have a better answer by then.
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tzenesJul 31 '10 at 18:12

1

community wiki? there isn't one right answer?
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McKayJul 31 '10 at 20:05

6 Answers
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Although this is somewhat subjective, i will make a list of things that i like more on SC2 than on SC1. (Warning, spoilers might be found here!):

atmosphere - i feel a lot more drawn into the game, all those references to the original story are also very cool + the large amount of ingame cutscenes and even mini-movies are awesome (the one with Zeratul and Kerrigan is my fav so far)

micromanagement of units - far better. Great management of groups, no limit of units per group (as far as i know). The ability to schedule commands is the best improvement in the game regarding control of units. A base can be build in a few clicks and you can focus on the fight nearby without interrupting to get back to the base and build the next building.

upgrades - clever design of upgrades, often you have to choose which one you want because you cant have all. In most games, when you are rich you simply buy everything and thats it. Not possible here (talking about the campaign).

better feel of the races - even more different units and structures than in SC1

saving - automatic saves at key points of the mission are handy. Not sure if this was in SC1 too but i think it was not.

single player - playing against a computer is now much better customized so choosing easy gives you really and easy game. This was not the case in SC1 where even the easiest oponent was tough for newbies. This was sometimes really frustrating.

I think thats it, there are more things which i think are better, but they are really too subjective.

AI Targeting - Units will naturally target enemy units they are more effective against

Damage Benefits - Armor Types from Warcraft 3 are included as Light or Armored (additionally, no type and biological are effective types) many units do increased damage to one type or another.

Increased Damage - Every unit that is a holder from Starcraft 1 does more damage (with the exception of the Zergling who will do more damage with the Improved Pathing).

High Ground - In SC1 high ground provided a chance of damage immunity per shot for ranged weapons. In SC2 this is gone, however units from low ground cannot shoot high ground units without vision (this was not true in SC1)

Smartcasting - As mentioned before the closest unit will cast a spell to the target. If that unit is already acting on such an order, the next closest unit is used and so on. This also means that the closest unit in a group tends to be drained of energy fastest.

Reduced Overkill - This is the biggest boost to units like Siege Tanks. Previously if one Zergling ran at 10 tanks, all 10 would fire on it (despite a single one being sufficient). In Starcraft 2, these units will coordinate and only 1 will fire.

Centered Splash Damage - With the exception of the Thor (who fires projectiles) all splash units center their splash radius on the center of their target. This is in contrast to splash originating from the closest point as in SC1.

Macro Mechanic - As detailed here every Race in SC2 has a unique Macro Mechanic to increase both unit production and economy.

Creep - Where as Creep functioned as a building platform in SC1, in SC2 it also increases Zerg unit move speed

Burrow - Ultralisks can now burrow, as well as the new Roaches and Infestors. Roaches and be upgraded to move while burrowed and Infestors start with this ability. This effectively gives Zerg invisible units

Overlords are not detectors - They must now be upgraded to Overseers (50 Minerals, 100 Gas) to work as detectors

When your main worker-producing structure dies you are revealed after a short time

Doodad blockers - There are doodads with HP that function as obstacles on many maps.

Xel'Naga Towers - There are neutral towers which are controlled by having a unit close to them (workers in these positions are not considered idle) giving sight to the surrounding area (range 11).

Customizable Decals - This is an Aesthetic feature.

Maps Start Explored - While fog of war is still present, the minimap will show the features of a map as the start of combat. In SC1 the map was initially blacked out. The SC2 Campaign still has maps blacked out.

LoS Blockers - Certain doodads act as line of sight blockers though do not hinder the passage of units.

Camera Mapping - The F4 through F9 keys can be used to map certain camera positions in the same manner as control groups.

Control Group Size Increased - Control Groups can now consist of 255 units, though only 200 will be displayed. These will be shown in numbered subgroups of 24 units each. The control group will also show the number of units in it on the HUD.

Multiple Building Selection - Multiple buildings can now be selected in the same manner as units. They can be queued at the same time and rallied at the same time. They may even be placed in control groups with other buildings or even units.

Waypoint - A similar waypoint system to Warcraft 3 exists where multiple actions can be set up. This includes things like abilities, and can even be used on rally points.

A few corrections (I can't edit). AI Pathing: Units do surround, but this happened in SC1; but as in SC1, units stop at maximum range, so other units have to walk around to surround. It'd be better if the units push forward to allow those in back to be in range, but they don't do that. High Ground: In SC1, you couldn't shoot at high ground without vision...but you got vision when a high-ground enemy shot at you. Control Group Size: 24 (3 rows of 8), not 36, are shown in a subgroup.
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KyralessaSep 15 '10 at 1:18

@Kyra so you're right about group size, but units actually wouldn't surround in SC1. The pathing AI was based on A* and didn't take into account units blocking nodes. As a result if your node was blocked along the path, you didn't move forward. If you did reach the last node before your target you would move to attack.
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tzenesSep 15 '10 at 8:05

"Maps Start Explored" in multilayer and custom games vs AI, but not in campaign.
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PiaskalSep 15 '10 at 10:18

For me, two of the most notable difference is the incorporation of convenient micromanaging features from Warcraft III, such as autocast and smartcast abilities (though to be honest the medic's "heal" from the original Starcraft was also autocast), and a more pronounced difference between the races.

Micromanagement features

Autocast allows you to toggle abilities that will be used automatically when necessary (such as heal, repair, build interceptors).

Smartcast means that when multiple units of the same type are selected and an ability is used, only one of the units will use the ability. Casting separately was one of the most difficult SC1 skills, now it's completely unnecessary. Priceless for force fields, storms, and for building units when multiple buildings are selected.

Finally, larger control groups and icons for control groups also help make things easier to manage.

Race difference

The original Starcraft already featured significant differences between the races, and Starcraft II builds on these differences. Creep is more important to Zerg because of the speed bonus; pylon placement is more important to Protoss because of the warp-in capabilities, etc. They also accented the differences by introducing different macro-enhancing abilities - the chrono-boost, mule and the queen's larva-spawning all help with macro, but each in a completely different way.

And yet, due to the nature of the rendering, it makes no difference. 1600x1200 won't show you more of the battlefield than 800x600; it'll just show you less blocky units.
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KyralessaAug 29 '10 at 18:51

+1 to Kyra's comment. As a matter of fact I did play in 800x600 because I hooked my laptop up to the tv through an s-video cable and that was the max supported resolution and it played just like normal with just slightly less crisp graphics.
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Davy8Sep 15 '10 at 13:16

Love the units. More units, and more challenges makes multiplayer more tactical. Different builds and "plans" put together in 2v2, 3v3 or 4v4 are what makes it for me. A buddy and I have a build where I mass phoenixes (AA) and he masses Colossi. Thus, he owns the ground, and any air I can own as well. I'm not sure if Starcraft 1 had leagues (Bronze, Silver, Gold, Platinum, Diamond, Masters, and Grandmasters), but it's fun to strive and ladder hard to make it to the next league, and show off.

The campaign is way easier to follow. You actually know what is happening to the character, like "Hey, Zerg is infiltrating a planet, let's protect the people", and not "Ok, I'm gonna kill the Gross Thingys, and then next mission I'll kill more".